Approximate Analytical Solutions of the Finite-Deflection Equations for a Shallow Spherical Shell

Approximate solutions are obtained, by Newton’s method, for shells subjected to uniform and/or point loads in the prebuckled or postbuckled configurations. Comparison of results with numerical solutions shows maximum deviations of 5 percent for clamped shells subjected to uniform loads in the prebuckled configuration. Similar comparisons for other cases show larger deviations. A characteristic load is developed which compares favorably with numerical buckling loads.